Prove that \( \sum_{m=0}^{n}{ }^{n} C_{m} \cdot \sin (m x) \cdot \cos (n-m) x=2^{n-1} \sin (n x) \)

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Prove that \( \sum_{m=0}^{n}{ }^{n} C_{m} \cdot \sin (m x) \cdot \cos (n-m) x=2^{n-1} \sin (n x) \)
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